A high-dimensional benchmark of objective functions and biological resolutions for personalized metabolic phenotyping

Abstract

Genome-scale personalized metabolic modeling relies on objective functions to simulate intracellular flux phenotypes, yet the optimal formulation for characterizing complex human diseases remains unknown. We ask which combination of objective function, biological resolution, and feature-selection strategy yields the most reliable diagnostic signal, treating machine-learning architecture as a controlled factor. We benchmarked these choices across 57 600 experimental configurations spanning six diverse pathologies, from oncology to neurodegeneration. Within this benchmark, pathway-level minimum reaction flux was the best-performing representation, indicating that diagnostic signals are more strongly associated with rate-limiting metabolic bottlenecks than with aggregate pathway activity. Under a leakage-free evaluation, diagnostic accuracy was largely insensitive to feature density (mean -score varying by <0.003 between the top-10% subset and the full feature space), so aggressive feature selection was not required. Among classifiers, only Logistic Regression lost accuracy at full density, whereas SVM was essentially unaffected and tree-based ensembles were resilient. Statistical regularization (robust_sigma) ensured consistent generalization, while topological objectives (local_k) were highly sensitive to metabolic noise, excelling only in specific high-signal cohorts. Finally, integrating objective function values as competitive features recovered the regulatory context lost during pathway aggregation. Accurate metabolic phenotyping was best captured by isolating restrictive bottleneck reactions. Predictive accuracy was largely insensitive to feature density; tree-based architectures tolerated dense omics data, while feature selection benefited mainly Logistic Regression. Overall, this benchmark offers systematic, evidence-based guidance for personalized metabolic modeling, complementing heuristic parameter tuning with quantitative comparison.

Background

Personalized metabolic modeling serves as a critical approach for decoding disease mechanisms. By leveraging comprehensive human network reconstructions like Recon3D [1], these frameworks predict intracellular flux distributions through flux balance analysis [2]. While maximizing biomass production is a validated objective for modeling unicellular organisms [3], defining the appropriate cellular goal for complex human diseases remains a context-dependent challenge.

Integrating patient-specific omics data into these models is essential for characterizing disease phenotypes [4]. However, a critical ambiguity remains: how do the mathematical formulation of the objective function and the granularity of the metabolic representation interact to define the metabolic differentiation? Previous studies indicate that modeling choices, whether prioritizing cellular energy, topological centrality, or statistical robustness, fundamentally alter the biological interpretation [5]. Yet, systematic evaluations have typically been limited to isolated parameters or microbial networks [6], leaving a quantitative gap in understanding how these variables collectively influence diagnostic accuracy in human pathologies.

In this study, we address this need by executing a high-dimensional benchmark that extends beyond alternative objective functions to evaluate the combinatorial interactions between biological resolution, machine learning architecture, feature selection strategy, and input composition. Utilizing 1143 samples across six diverse pathologies, including oncology, neurodegeneration, and metabolic syndromes, we analyzed 57 600 unique experimental configurations. As illustrated in Fig. 1, our study design systematically permutes seven dimensions categorized into three main modules: the biological context, the metabolic modeling core, and the machine learning engine. This systematic approach allows us to characterize design trade-offs in metabolic phenotyping, providing benchmark-based guidance for selecting objective functions, resolutions, and sparsity levels for clinical biomarker discovery. By systematically quantifying the impact of these methodological choices, this benchmark provides a standardized reference to guide the reliable design and execution of future metabolic modeling studies. Concretely, the benchmark is organized around one primary research question: which objective function and biological resolution best support diagnostic classification, with feature selection, input composition, and model architecture evaluated as supporting dimensions rather than co-equal endpoints. We study several principles including the relevance of rate-limiting reactions, the benefits of feature selection, and the robustness of tree-based models in high-dimensional settings that are known in the literature. Our main contribution is therefore the systematic, large-scale quantification and joint comparison of these choices across diverse human pathologies, rather than the discovery of fundamentally new principles. This paper is organized as follows. The next section presents the results from different benchmarking experiments. In the Discussion, we consider the implications of our findings along with their limitations. Then, we conclude with a summary of key points. Finally, we present the methodological details of our benchmark in the last section.

Figure 1.

Hierarchical overview of the experimental benchmarking architecture, in which seven experimental dimensions, grouped into Biological Context (datasets), Mathematical Modeling (objectives, resolutions) and Machine Learning Engineering (input, models, selectors, density), are permuted to yield 57 600 unique validation scenarios.

Methods

Data acquisition and preprocessing

To ensure the generalizability of our benchmarking, we selected six diverse metabolomics datasets representing distinct metabolic etiologies, including oncology, neurodegeneration, and metabolic syndromes (Table 1). The combined cohort consists of 1143 samples.

Table 1.

Characteristics of benchmarked metabolomics datasets.

Dataset ID	Pathology	Total N	H/P	Reference
BC	Breast cancer	214	95/119	[7]
BRCA-ATLAS	Breast cancer	132	65/67	[8]
PRAD-ATLAS	Prostate cancer	223	96/127	[8]
PDAC-ATLAS	Pancreatic cancer	59	26/33	[8]
Alzheimer	Alzheimer’s disease	229	71/158	[9]
Diabetes	Diabetes mellitus	286	82/204	[10]

Since computing metabolic log-fold changes requires complete and strictly positive numerical inputs, missing or zero values had to be handled before analysis. Most datasets (BC, BRCA, PDAC, Alzheimer’s, and Diabetes) were acquired in a pre-imputed state. For these, any residual missing values were simply replaced with the minimum detected abundance for the respective metabolite.

The PRAD-ATLAS dataset contained significant sparsity in its raw form. To address this, samples with >50% missing values were excluded from the analysis. For the remaining samples, missing or zero values were imputed using a half-minimum strategy, replacing them with 50% of the minimum positive value detected for each specific metabolite. In these targeted metabolomic panels, missing or zero entries denote non-detection events—indicating abundances below the platform’s detection limit—rather than true biological absence. Consequently, these entries were imputed with a small positive floor value rather than treated as absolute zeros. The pre-imputed datasets retained only sparse residual non-detections, for which the per-metabolite minimum detected abundance served as an adequate floor. For the substantially sparser PRAD-ATLAS dataset, a more conservative half-minimum floor was applied to prevent imputed values from coinciding exactly with the detection threshold. Because these floors are implemented as per-metabolite constants, they function similarly to other cohort-level statistics within the pipeline, where recomputation within each training fold shifts the mean score by <0.001 (Section Machine learning pipeline and feature selection).To assess the sensitivity of our findings to the imputation strategy, we evaluated four distinct methods across the three ATLAS cohorts available in raw, pre-imputation form (PRAD, BRCA, and PDAC): the per-metabolite minimum, the half-minimum, k-nearest neighbors (k=10), and a mechanism-aware hybrid approach. In the hybrid strategy, each metabolite was classified as either left-censored (missing not at random, MNAR) or missing completely at random (MCAR) based on whether samples with missing values exhibited a significantly lower overall signal, determined using a one-sided Wilcoxon test on per-sample median abundances (P <.05). MNAR metabolites were imputed using quantile regression for left-censored data (QRILC), whereas MCAR metabolites were imputed via k-nearest neighbors. This classification identified 146 of 476, 329 of 536, and 47 of 355 metabolites as MNAR in PRAD, BRCA, and PDAC, respectively. Mean performance remained stable across all four strategies, with narrow ranges of 0.012, 0.003, and 0.025 across the three datasets. Furthermore, pathway-level resolutions remained top-ranked or statistically equivalent, with configuration-specific differences between the hybrid approach and simpler floor methods averaging . These results demonstrate that the downstream conclusions are robust to the choice of imputation method.

Metabolitics framework overview

As a testbed, we perform our benchmarking experiments within the Metabolitics framework [7], which integrates metabolomics data into genome-scale metabolic models in a personalized manner. In this study, we utilize the Recon3D [1] human metabolic reconstruction as the scaffold network. Intracellular metabolic rewiring is predicted by incorporating personalized fold-changes into the objective function of a flux variability analysis (FVA) [11] task. To focus on specific pathways and reduce network noise, transport reactions and highly connected hub reactions (i.e. involving >10 metabolites) were excluded from the objective function formulation. Because a linear programming optimum is not necessarily unique, we avoided selecting a single arbitrary flux vertex. Instead, for each reaction, the feature was defined as the midpoint of its FVA interval, , evaluated over the optimal face with the objective function pinned at its optimal value. This framing bounds the influence of alternative optimal solutions to by construction. All flux variability problems were solved using IBM CPLEX (version 22.1.2) under deterministic solver settings.

Notation and formalism

We define the following mathematical conventions used throughout the benchmarking framework:

• : the stoichiometric matrix of the Recon3D network, where M is the number of metabolites and R is the number of reactions.

• : the vector of reaction fluxes.

• : the personalized metabolic log-fold change for metabolite m in individual i.

• : the set of reactions involving metabolite m within its defined pathway or subsystem.

• : the set of measured metabolites produced by reaction r.

• : the set of reactions within a k-hop neighborhood of metabolite m in the stoichiometric graph.

• : the measurement confidence weight derived from the standard deviation () of metabolite m across the cohort.

Personalized objective functions

Let be the stoichiometric matrix. For each individual i, the personalized metabolic log-fold change (mfc) for metabolite m is defined as , where is the measured concentration of metabolite m in individual i, and is the mean concentration of the same metabolite across the healthy cohort. We benchmarked six distinct families of objective functions to incorporate these fold-changes into the objective function of an FVA instance:

(1)

In this formulation, is the vector of reaction fluxes, is the vector of objective coefficients () for each reaction r, while and denote the lower and upper bounds of the flux capacities, respectively.

To prevent numerical instability in linear programming solvers, all calculated objective coefficients were scaled by a global factor .

Baseline: global stoichiometric mapping

The standard approach distributes the influence of a metabolite to all reactions producing it (), normalized by the total stoichiometry of the associated reactions ():

(2)

where is the set of measured metabolites produced by reaction r, represents the stoichiometric coefficient of metabolite m in reaction r, and is the set of all reactions involving metabolite m within its defined biological subsystem.

Local pathway activity (k-hop)

This objective restricts the influence of a metabolite to its topological neighborhood. A metabolite affects a reaction only if that reaction lies within k steps in the metabolic graph. The weight is distributed equally among reactions in the neighborhood:

(3)

where is the set of reactions within a k-hop distance of metabolite m, and represents the total number (cardinality) of reactions in that neighborhood. We benchmarked . To ensure biological context, currency metabolites (e.g. ) and hubs connected to >50 reactions were excluded from neighborhood expansion.

Robust optimization (noise-aware)

To mitigate measurement noise, reaction weights are regularized by the standard deviation () of each metabolite across the healthy control cohort:

(4)

where is the standard deviation of metabolite m in the healthy cohort, and is the regularization threshold. The final coefficient is derived as

(5)

in which acts as the measurement confidence weight for metabolite m.

Topology centrality

This method weights reactions according to their global network importance using PageRank centrality () [12]. Centrality scores were normalized such that the mean weight across all reactions equals 1.0:

(6)

where is the PageRank centrality score of reaction r, and is the coefficient calculated via the baseline mapping.

Biological constraints (energy and growth)

These formulations introduce cellular maintenance goals as either objective terms or constraints:

• ATP maximization: a weighted term for the ATP maintenance reaction () is added: , where is the flux of the ATP maintenance reaction and is the weight assigned to energy production.

• Biomass constraint: ensures a minimum growth threshold: , where is the biomass production flux, is the theoretical maximum growth rate, and is the minimum viability threshold.

Feature extraction and multi-resolution aggregation

The output of the FVA provides a feasible flux range for each reaction. The personalized metabolic state is represented by the midpoint of this range, . To evaluate the impact of biological granularity, fluxes were aggregated into six resolutions. For a pathway P containing reaction set , the pathway-level feature is calculated as:

• Reaction:   (the raw flux value).

• Pathway_min:   (the rate-limiting bottleneck).

• Pathway_mean/median/max/sum: calculated using standard aggregation metrics across .

Machine learning pipeline and feature selection

Classification was performed separately within each of the six datasets as a binary healthy-versus-patient task (label 1 = patient, 0 = healthy control), using 10-fold stratified cross-validation; the 1143 samples are the combined size of these six independent per-dataset analyses. Reported F1-scores are computed per dataset and then averaged across the six diseases. Datasets were not pooled into a single joint classifier. We evaluated two input configurations: (i) Flux Only, and (ii) Flux + Coefficients (), where the patient-specific mathematical weights derived dynamically in Phase 1 are concatenated to the simulated flux vector. For each configuration, a 10-fold stratified cross-validation scheme was implemented. The pipeline benchmarked four architectures: Random Forest (100 trees) [13], XGBoost [14], Logistic Regression with L2 regularization, and Linear SVM [15].

To assess the stability of metabolic drivers while avoiding information leakage, feature selection and standardization were performed entirely within each cross-validation fold separately rather than on the full cohort. Parametric (ANOVA F-test) and nonparametric (Wilcoxon Rank-Sum [16]) selectors were used to rank features, which were then filtered through five density thresholds: 10%, 20%, 50%, P <.05, and Full (100%). For every training partition, features were ranked and filtered, and StandardScaler was fit on the training samples only and then applied to the held-out fold. The healthy-cohort mean () and robust standard deviation () used to construct the personalized coefficients were estimated once from the healthy controls of each cohort and therefore enter the pipeline as an external population reference. Model performance was quantified using the F1-score, specifically targeting the accuracy of disease-state identification. For every configuration, we report the mean across the six datasets together with its 95% confidence interval (normal approximation over configurations), as well as ROC-AUC and PR-AUC. To interpret the small differences observed between top-performing resolutions, we report paired effect sizes (Cohen’s d) calculated across matched configurations—defined as models sharing identical objective functions, input compositions, feature selectors, densities, and underlying models, and differing solely in their biological resolution—alongside Wilcoxon signed-rank tests. Effect sizes are prioritized over nominal P-values because the large number of matched configurations renders even negligible performance differences statistically significant.

Computational implementation and environment

The benchmarking framework was implemented in Python, utilizing the COBRApy [17] library for metabolic modeling and Scikit-learn [18] for machine learning tasks. Experiments were executed on the TRUBA High-Performance Computing cluster using the barbun partition. To manage the 57 600 unique experimental combinations, a parallel execution strategy was employed across 40 CPU cores per node, with individual processes restricted to two threads (OMP_NUM_THREADS=2). Linear programming problems were solved with high precision using the IBM CPLEX (v22.1.1) solver.

Use of artificial intelligence–assisted technologies

During the preparation of this work, the authors employed large language models to refine the English language readability, enhance the structural flow of the discussion, and polish the academic phrasing of the manuscript. Following the use of these tools, the authors extensively reviewed, edited, and validated the resulting text to ensure scientific accuracy and consistency. The authors declare that they take full responsibility for the scientific integrity, data interpretation, and final content of the publication.

Results

Impact of biological resolution

Because the benchmark spans several conceptually distinct stages of the analytical pipeline, Table 2 maps each benchmarked dimension to its corresponding pipeline stage and specific sub-question. This distinguishes the primary exploratory questions, namely, the objective function and biological resolution, from the supporting dimensions. The first dimension of the benchmark evaluates the impact of feature granularity by comparing reaction-level and pathway-level models. The reaction-level feature space utilizes 10 600 individual flux capacities, representing the rawest form of metabolic data. Aggregation into pathways reduces this dimensionality to 106 features based on biological subsystems. This experiment aims to determine whether direct reaction fluxes or pathway scores derived through various aggregation metrics provide a more stable diagnostic signal. The primary evaluation of six metabolic resolutions establishes a clear performance hierarchy based on the global mean F1-score: Pathway_min (0.7930) > Reaction (0.7915) > Pathway_mean (0.7896) ≈  Pathway_sum (0.7896) > Pathway_median (0.7833) > Pathway_max (0.7831)(Table 3). Although the absolute performance margins are narrow, Pathway_min achieves the highest mean . Its margin over the Reaction resolution is modest and not statistically significant (Wilcoxon signed-rank test [16], P=.16), whereas its superiority over the remaining pathway aggregations is statistically significant despite a small effect size. This pattern suggests that capturing the ”bottleneck” reaction, the rate-limiting step within a metabolic pathway, provides a more reliable phenotypic signal than standard central tendency measures. Although Pathway_min attains the highest mean (0.7930), its advantage over the Reaction resolution is not statistically distinguishable (Cohen’s d=0.04, P=.16), and its advantage over Pathway_sum/Pathway_mean, while significant, is of small effect size (d≈ 0.10). The clearer separation is against the median and maximum aggregations (d≈ 0.25–0.28). While still maintaining this nearness, the threshold-independent metrics arrange the two best-performing techniques in a different fashion: Reaction wins both the ROC-AUC (0.7656) and PR-AUC (0.8380), while Pathway_min achieves the best results with F1 (see Table 4). This discrepancy can be explained by the fact that there is no substantial difference in the F1 scores of the techniques, while the median and maximum aggregations rank lowest under all three metrics.

Table 2.

The benchmarked dimensions, the pipeline stage at which each acts, and the sub-question it addresses, with the objective function and biological resolution as the primary endpoints and the remaining dimensions as controlled supporting factors.

Dimension	Pipeline stage	Sub-question addressed	Role
Objective function (baseline, ATP, biomass, robust, local)	Constraint-based modeling (defines )	Which personalization of the FVA objective yields the most reliable diagnostic signal?	Primary
Biological resolution (Reaction; Pathway min/sum/mean/median/max)	Feature construction/aggregation	At what biological granularity should fluxes be summarized for classification?	Primary
Input composition (Flux versus Flux+Coeff)	Feature construction	Does adding the objective-coefficient “regulatory weight” improve prediction?	Supporting
Feature selection & density (selector, 10–Full)	Dimensionality reduction	How much sparsity is needed, and does it depend on the model?	Supporting
ML architecture (LR, SVM, RF, XGB)	Classification	Which model class best exploits high-dimensional metabolic features?	Controlled

Table 3.

Global performance audit across biological resolutions.

Resolution	Mean F1	Median F1	Std Dev	CV (%)
Pathway_min	0.7930	0.7957	0.0861	10.9
Reaction	0.7915	0.7930	0.0911	11.5
Pathway_mean	0.7896	0.7945	0.0843	10.7
Pathway_sum	0.7896	0.7946	0.0842	10.7
Pathway_median	0.7833	0.7981	0.0849	10.8
Pathway_max	0.7831	0.7933	0.0883	11.3

Bold indicates the highest mean F1-score.

Table 4.

Threshold-independent discrimination across biological resolutions, each with a 95% confidence interval over benchmark configurations where F1 values match Table 3 and ROC-AUC and PR-AUC complement the F1-based ranking.

Resolution	Mean F1 (95% CI)	ROC-AUC (95% CI)	PR-AUC (95% CI)
Pathway_min	0.7930 ± 0.0017	0.7471 ± 0.0027	0.8213 ± 0.0017
Reaction	0.7915 ± 0.0018	0.7656 ± 0.0024	0.8380 ± 0.0015
Pathway_mean	0.7896 ± 0.0017	0.7499 ± 0.0026	0.8291 ± 0.0015
Pathway_sum	0.7896 ± 0.0017	0.7499 ± 0.0026	0.8290 ± 0.0015
Pathway_median	0.7833 ± 0.0017	0.7291 ± 0.0026	0.8072 ± 0.0016
Pathway_max	0.7831 ± 0.0018	0.7360 ± 0.0027	0.8178 ± 0.0016

The Reaction resolution demonstrated the highest model sensitivity (0.0381), with performance dropping under linear models such as logistic regression (0.7676) compared with nonlinear ensemble learners like XGBoost (0.8057). This variance yielded the study’s highest coefficient of variation (), defined as the ratio of the standard deviation to the mean (). In contrast, Pathway_min effectively stabilized the feature space, reducing the performance gap between linear and nonlinear models to 0.0186. This stability ensures that the biological signal remains consistent across different modeling approaches, regardless of the classifier’s complexity.

In terms of computational efficiency, the transition from 10 600 reaction features to 106 pathway-level features resulted in a 100-fold reduction in dimensionality. This substantially reduces machine-learning training cost without any loss in predictive accuracy. These results show that biological aggregation effectively removes redundant data while preserving the core diagnostic information.

The impact of input composition also varied across resolutions. While Reaction-level modeling gained only 1.34% from the inclusion of reaction coefficients (), Pathway_median and Pathway_sum showed higher improvements of 3.23% and 2.66%, respectively. This indicates that while reaction fluxes already reflect stoichiometry, explicitly adding these weights becomes important at the pathway level to maintain the biological context that is otherwise lost when reactions are averaged or summed.

The objective functions

We evaluated 20 variations of objective functions, following a specific naming convention, [method_name]_[parameter]_[value] to delineate the hyperparameter space tested for each function family. For example, atp_atp_10.0 denotes the ATP maximization method with a specific weight (λ) of 10.0, while baseline_base denotes the standard unweighted Metabolitics objective function. These 20 variations are categorized into four functional families as follows:

• Global Family: includes the standard baseline_base mapping and the PageRank-weighted topology_base [12].

• Topological Family: consists of six local_k methods, representing neighborhood expansion depths from k=1 to k = 6.

• Statistical Family: comprises four robust_sigma variations utilizing variance-based regularization thresholds of .

• Biological Family: includes four ATP maximization objectives (atp_atp) with weights of and four biomass-constrained objectives (biomass_bio) with viability thresholds of .

Globally, the robust_sigma family leads the ranking, with robust_sigma_0.01 and robust_sigma_0.1 effectively tied at the top (mean F1-scores of 0.7919 and 0.7918). Statistical tests confirm that the improvements offered by variance based weighting over the baseline are highly significant (FDR-adjusted ), indicating that noise-aware modeling is a more robust generalist strategy for multi-disease characterization within this benchmark.

Despite the global dominance of statistical methods, topological objectives emerge as high-precision specialists under specific conditions. In oncological contexts such as Breast Cancer (BC) and BRCA, deeper neighborhood information (e.g. local_k6) yielded the highest diagnostic scores. However, these methods exhibit high sensitivity to the underlying model architecture, performing optimally with ensemble learners while showing a significant performance decay under linear constraints.

Among the topological objectives, intermediate neighborhood depths provided the strongest signal: local_k2 was the best-ranked topological method overall (Fig. 2), whereas deeper expansions (local_k4–local_k6) ranked among the lowest, indicating that excessive network expansion is increasingly sensitive to noise

Figure 2.

Objective function performance across all 57 600 experiments, with bars showing the mean -score for each objective function with 95% confidence intervals over configurations; the robust_sigma family ranks the highest.

Parameter sensitivity and method stability

To evaluate the reliability of these findings, we performed a sensitivity audit across the hyperparameter space (Fig. 3).

Figure 3.

Parameter sensitivity landscape across four objective function families: (A) Topological methods (local_k) peak at k=2 and decline at greater neighborhood depths; (B) Robust optimization (robust_sigma) is stable for and declines at; σ =0.5 (C) ATP maximization (atp_atp) is largely insensitive to weight (λ); (D) Biomass constraints (biomass_bio) show marginal variation.

Topological methods exhibited severe structural volatility, with a statistically significant performance gap () between optimal and suboptimal topological depths (k). While the global average peaked at k=2 (0.7897), the optimal neighborhood radius fluctuated drastically across diseases, ranging from k=1 in Diabetes to k=6 in BRCA. This lack of parameter transferability indicates limited cross-disease generalization for any single neighborhood depth. While this may reflect overfitting to dataset-specific network topology, it could equally arise from disease-specific metabolic re-organization or tissue-dependent network properties. Consequently, we regard deep topological methods as exhibiting reduced transferability rather than definitive overfitting.

In contrast, statistical regularization was stable across its tested range, with the best performance at low σ (). The sensitivity index, defined as the maximum percentage deviation in mean F1-score across a parameter’s tested range, remained low (0.45%) for robust methods, indicating a predictable and safe operating range () that does not require disease-specific tuning.

Remarkably, biological objectives demonstrated near-total insensitivity to parameter magnitude, with ATP maximization showing a negligible sensitivity index of 0.05%. Crucially, this stability implies a lack of discriminative gain; Wilcoxon tests confirmed that neither ATP maximization (P=.27 for λ =100) nor Biomass constraints (P=.59 for γ =0.2) yielded a statistically significant improvement over the baseline. This lack of significance suggests that the solution space is structurally constrained by the stoichiometric network topology itself, rendering the classification performance largely unaffected by the magnitude of biological objective coefficients.

Computational efficiency and the pareto frontier

Beyond predictive performance, we evaluated the clinical feasibility of each objective function through a computational efficiency audit (Fig. 4, Panel C). Our results identify a clear Pareto frontier where statistical robustness provides the optimal trade-off between diagnostic accuracy and resource consumption.

Figure 4.

Framework performance interactions and efficiency: (A) Impact of feature density on machine learning model performance across architectures; (B) Relative performance gain achieved by integrating objective function coefficients () across different resolutions; (C) Computational efficiency Pareto frontier, representing total running time versus global mean F1-score; (D) Distribution of -scores across benchmark configurations for each biological resolution, summarizing the systemic volatility of each feature space.

The robust_sigma family occupies the most efficient region of the frontier, with robust_sigma_0.1 maintaining peak F1-scores at a median running time of . In contrast, topological methods exhibit a near-linear increase in computational overhead as neighborhood depth (k) expands. Moving from the baseline to local_k6 results in a 54.3% increase in total running time ( versus ) and a significant rise in peak memory usage (≈ 7454 MB versus ≈ 5028 MB).

This computational penalty is not compensated by a global accuracy gain; in fact, the highest-cost method (local_k6) yielded a lower aggregate F1-score than the most efficient statistical variants. These findings suggest a saturation point in metabolic network modeling, where increasing the topological search radius beyond k=2 leads to diminishing returns both in terms of predictive power and high-performance computing throughput. Consequently, for large-scale multi-disease characterization, variance-based weighting offers a more scalable and cost-effective alternative to high-depth neighborhood expansion.

Machine learning model robustness

Among the four classifiers evaluated, Random Forest (RF) [13] yielded the highest global mean F1-score (0.7996), followed by SVM [15] (0.7936) and XGBoost [14] (0.7885). Logistic Regression (LR) was the weakest classifier (0.7717). Statistical analysis (Wilcoxon signed-rank test) confirmed that these performance differences are significant across all pairwise comparisons (FDR-adjusted ).

As shown in Fig. 4 (Panel A), the models responded differently to feature density. Logistic Regression declined when moving from the top 10% features to the full dataset (0.7835 to 0.7623), whereas SVM was essentially unaffected. In contrast, the tree-based ensembles improved with additional features: RF rose from 0.7914 to 0.8035 and XGBoost from 0.7781 to 0.7963. This resilience is fundamentally rooted in how these models handle the feature space. Unlike linear models that attempt to optimize weights across the entire 10 600D space simultaneously, tree-based ensembles utilize feature subsampling to construct individual trees from small, random subsets of the total features, therefore never working with the whole feature space altogether. This approach makes them effectively bypass the Curse of Dimensionality [19] that hampers linear classifiers.

Aggregation into pathways acted as a modest noise filter for LR, which improved by roughly 1% at the pathway level (from 0.7676 at the reaction level to 0.7765 for Pathway_mean). However, high-capacity models like XGBoost appeared to extract useful diagnostic information from fine-grained reaction fluxes that are lost during aggregation, as evidenced by its superior performance at the reaction level. The optimal resolution varied by model architecture. While RF performed similarly across resolutions, LR required pathway-level aggregation to maximize accuracy. On the other hand, XGBoost was the only model to favor reaction-level features, suggesting it can leverage the full granularity of the metabolic network better than other architectures. The corresponding dispersion of F1-scores across configurations for each resolution is summarized in Fig. 4, Panel D.

Performance gains via input composition

We evaluated the contribution of objective function coefficients () by introducing them as competitive features alongside metabolic fluxes. This hybrid input configuration yielded a statistically significant global performance increase of 2.28% (FDR-adjusted ), with -inclusive models outperforming flux-only models in 71.2% of all experimental scenarios ( versus wins).

The utility of coefficients was highly dependent on biological resolution (Fig. 4, Panel B). At the Reaction level, the inclusion of provided a marginal gain of 1.34%. However, at aggregated resolutions, this benefit increased notebly, peaking at 3.23% for the Pathway_median resolution. Consistent with this trend, feature-selection analysis showed that values accounted for 33.5% of the selected features at the reaction level, rising to 49.6% at the pathway level.

Crucially, feature importance analysis demonstrates that objective coefficients are not merely supplementary features but high-impact discriminators. On average, selected features carried 1.26× the Random-Forest importance of raw fluxes (mean importance 0.021 versus 0.017). This dominance was most pronounced in the BC dataset, where coefficients were 1.86× more impactful than fluxes in defining the decision boundary. This suggests that the “regulatory weight” assigned by the objective function may serve as a more informative predictor of the disease state than the reaction rate itself within these datasets.

A head-to-head comparison of feature selection frequency (Table 5) further reveals a distinct regulatory preference. While raw fluxes were selected more frequently on a global scale (Ratio: 0.63×), the model preferentially selected coefficients over fluxes for specific metabolic subsystems. Notably, Tetrahydrobiopterin metabolism showed a 1.67× preference for coefficients, followed by Glycerophospholipid (1.42×) and Alanine and aspartate metabolism (1.28×). This indicates that for these specific pathways, the objective weight () provided a stronger discriminative signal than the computed flux outcome.

Table 5.

Feature selection preference: flux versus coefficient () in top-ranked pathways.

Metabolic subsystem	Flux count	Coeff () count	Ratio (C/F)
Tetrahydrobiopterin metab.	22 767	37 957	1.67x
Glycerophospholipid metab.	27 926	39 573	1.42x
Fatty acid synthesis	26 803	36 050	1.35x
Citric acid cycle	27 007	36 187	1.34x
Alanine and aspartate metab.	28 072	35 972	1.28x
All subsystems (total)	58 611 107	37 037 940	0.63x

Bold indicates ratios greater than 1, i.e. subsystems for which coefficients were selected more frequently than fluxes.

Selector sensitivity

The choice of feature selection strategy, comparing the parametric ANOVA (F-test) against the nonparametric Wilcoxon Rank-Sum test, reveals a high degree of performance parity within the framework. Globally, the performance delta between the two selectors is marginal, with a mean F1-score difference of only 0.0003. This statistical equality suggests that the primary diagnostic signals captured by the objective functions are robust to the underlying selection filter.

However, when we delve in deeper, there is a compositional divergence. While both selectors yield near-identical predictive accuracy, their internal selection logic varies significantly depending on the biological resolution. At the aggregated pathway level, the ANOVA and Wilcoxon selected sets showed moderate agreement (median Jaccard overlap 50.9%; Cohen’s κ = 0.50 on set membership), indicating a substantial but incomplete convergence on a shared metabolic core.

This partial overlap reflects a degree of functional redundancy, where the two selectors capture the same phenotypic state through partly divergent yet overlapping metabolic signatures. Consistent with their near-identical predictive accuracy (mean difference 0.0003), the ranking of objective functions was unchanged between selectors; only their mean -scores differed marginally.

Impact of feature density

In this part, we evaluate the relationship between feature density and diagnostic performance. Under leakage-free evaluation, global performance was largely insensitive to feature density: the mean F1-score varied by <0.003 across the entire range, from 0.7865 at the 10% threshold to a peak of 0.7894 at 20% density, with the full feature set reaching 0.7883 (Table 6). Aggressive feature selection therefore provided no global advantage over using the full feature space.

Table 6.

Performance audit across feature densities.

Density	Mean F1	CV (%)
10% (Top-k)	0.7865	11.11
20%	0.7894	10.92
P <.05	0.7886	10.95
50%	0.7890	10.99
Full (100%)	0.7883	10.94

Bold indicates the highest mean F1-score.

This near-invariance to density held across resolutions. In the high-dimensional Reaction space (10 600 features) the gap between 10% and full density was only 0.012, and at the low-dimensional Pathway_min resolution (106 features) it was negligible (<0.001). Thus the bottom 90% of features neither substantially helped nor harmed global performance, indicating that the diagnostic signal is concentrated in a small, robust feature core rather than being governed by the selection threshold. Model architecture nonetheless modulated this response. Logistic Regression was the only classifier to lose accuracy at full density (a 2.71% decline), consistent with the curse of dimensionality [19] affecting a purely linear decision boundary. SVM was essentially unaffected (+0.23%), while the tree-based ensembles benefited from the additional features (Random Forest +1.53%, XGBoost +2.33%). Consequently, feature selection is not required for good performance in this framework; it offers a modest benefit only for Logistic Regression.

Biological validation of discovered features

To validate the biological fidelity of the framework, the top-ranked features (pathways) extracted from unrestricted density models were evaluated against two independent modalities: clinical transcriptomic data obtained from a multimodal pan-cancer atlas [8] and an established set of canonical breast cancer pathways curated from literature. For the independent transcriptomic validation, statistically selected pathways were mapped to their constituent genes via Gene-Protein-Reaction rules to calculate the percentage of significantly differentially expressed genes (FDR < 0.05). We report the fraction of differentially expressed genes per pathway as a descriptive concordance measure, but base our inferential claims on permutation and hypergeometric-enrichment tests, which control for pathway size and the genome-wide differential-expression rate. To provide an interpretable foundation for the transcriptomic overlap, we benchmarked it using two approaches. First, compared with a permutation null model consisting of random gene sets of matched size, the maximum per-pathway differential expression fraction did not exceed chance levels individually in any cohort (). This occurs because raw overlap percentages are inflated by small pathways and by each dataset’s baseline genome-wide differential expression rate (which ranged from 8.6% to 49%); thus, an unadjusted figure such as 63% lacks independent interpretability. Second, size-corrected hypergeometric enrichment (Benjamini–Hochberg FDR) recovered biologically coherent, disease-specific concordance in three of five pathologies: fatty-acid oxidation and tryptophan metabolism in BRCA; pyruvate metabolism, the TCA cycle, fatty-acid oxidation, and branched-chain amino-acid metabolism in clear-cell renal carcinoma (reflecting its canonical reprogramming); and purine synthesis in PRAD. In contrast, no pathways survived FDR correction in COAD and PDAC, which is consistent with their exceptionally high baseline differential expression rates (∼45–49).

Independent transcriptomic validation was performed for the cohorts with matched transcriptomes (BRCA, PRAD, and the enrichment set comprising BRCA, PRAD, PDAC, COAD, and ccRCC), while curated literature concordance was assessed across all five pathologies. We do not extend these validation claims to datasets lacking matched molecular data. In the literature concordance analysis, performance was measured using Precision, Recall, and F1-score against the literature-derived pathway sets. Expanding our evaluation across five diverse pathologies (Table 7), the framework yielded a maximum per-disease F1-score of 0.444 (in the PRAD cohort), with comparable retrieval in Diabetes (0.421). For this specific oncology cohort, the consensus set of retrieved pathways included Alanine and aspartate metabolism, Arginine and proline metabolism, Taurine and hypotaurine metabolism, CoA catabolism, Nucleotide interconversion, Biotin metabolism, Glycolysis/gluconeogenesis, Eicosanoid metabolism, CoA synthesis, and Aminosugar metabolism [20–24]. Beyond breast cancer, the framework successfully captured disease-specific ground truths. In prostate cancer (PRAD), it retrieved a comprehensive set of metabolic alterations including Citric acid cycle, Fatty acid synthesis, Fatty acid oxidation, Cholesterol metabolism, Alanine and aspartate metabolism, Arginine and proline metabolism, Sphingolipid metabolism, and Glycolysis/gluconeogenesis (Max F1: 0.444) [25–33]. In pancreatic cancer (PDAC), hallmarks of KRAS-driven rewiring were identified, specifically Glycolysis/gluconeogenesis, Pentose phosphate pathway, Alanine and aspartate metabolism, Aminosugar metabolism, Purine synthesis, and Pyrimidine synthesis (Max F1: 0.250) [34–40]. For Alzheimer’s disease, prioritized features included Oxidative phosphorylation, Glycolysis/gluconeogenesis, Cholesterol metabolism, and Sphingolipid metabolism (Max F1: 0.429), aligning with the mitochondrial cascade hypothesis and lipid dysregulation [41–52]. Finally, in diabetes mellitus, the framework correctly isolated a broad spectrum of metabolic dysregulations including Valine, leucine, and isoleucine metabolism, Glycerophospholipid metabolism, Sphingolipid metabolism, Glycolysis/gluconeogenesis, Fatty acid oxidation, Phenylalanine metabolism, Tyrosine metabolism, Alanine and aspartate metabolism, and Oxidative phosphorylation (Max F1: 0.421) [53–61].

Table 7.

Cross-disease canonical pathway retrieval summary.

Disease	Mean F1	Max F1	Max True Positives (TP)	Evaluated Configs.
Diabetes mellitus	0.1943	0.4211	4 out of 10	1600
Breast cancer (BC)	0.1479	0.3158	3 out of 10	3200
Pancreatic cancer (PDAC)	0.1143	0.3750	3 out of 10	1600
Prostate cancer (PRAD)	0.1021	0.4444	4 out of 10	1600
Alzheimer’s disease	0.0316	0.2857	2 out of 10	1600

Evaluation of input configurations indicated a stark contrast to initial assumptions: models utilizing coefficient-integrated inputs () significantly outperformed those relying only on raw flux vectors across the datasets (e.g. FDR-adjusted in BC and PDAC). Furthermore, the impact of machine learning architectures exhibited disease-dependent dynamics. Nonlinear architectures (Random Forest, XGBoost) demonstrated superior biomarker retrieval in highly combinatorial pathologies such as Breast Cancer and Alzheimer’s, whereas linear approaches (Logistic Regression) excelled in retrieving validated pathways for direct metabolic syndromes like Diabetes, reflecting the univariate statistical origins of their respective reference markers.

In addition, to identify the optimal mathematical formulation for biological discovery, we aggregated the literature concordance performance of each objective function across all pathologies. Table 8 ranks the evaluated methods by their global mean F1-score. The results identify the Statistical family (robust_sigma) as the top-performing group for literature concordance, led by robust_sigma_0.05 (mean 0.1566), with topology_base a close second (0.1503). The Biological family, particularly variants of ATP maximization and biomass constraints, showed high consistency, occupying most of the top-tier rankings. Interestingly, while the Statistical family (robust_sigma) provided stable results, it was slightly outperformed by the global and biological benchmarks in terms of literature alignment. In contrast, the Topological family exhibited a clear performance decay as neighborhood depth increased; local_k1 remained competitive, but higher depths such as local_k4 and local_k5 yielded the lowest concordance scores, suggesting that excessive network expansion introduces noise that obscures canonical metabolic signals.

Table 8.

Global benchmark of objective functions against literature ground truths aggregating F1-scores across all evaluated pathologies and ranking methods by global mean F1-score to identify the most reliable formulations for canonical pathway retrieval.

Function family	Objective method	Global mean F1	Global median F1	Std. dev
Statistical	robust_sigma_0.05	0.1566	0.1429	0.0906
Global	topology_base	0.1503	0.2105	0.1059
Statistical	robust_sigma_0.1	0.1455	0.1429	0.0967
Statistical	robust_sigma_0.5	0.1433	0.1333	0.0916
Statistical	robust_sigma_0.01	0.1364	0.1333	0.0699
Topological	local_k2	0.1265	0.1053	0.1324
Topological	local_k6	0.1263	0.1111	0.0972
Topological	local_k1	0.1262	0.1333	0.0869
Global	baseline_base	0.1173	0.1176	0.0916
Biological	biomass_bio_0.1	0.1170	0.1111	0.0916
Biological	atp_atp_50.0	0.1159	0.1111	0.0931
Biological	atp_atp_10.0	0.1155	0.1111	0.0914
Biological	atp_atp_1.0	0.1106	0.1111	0.1080
Biological	biomass_bio_0.01	0.1070	0.1111	0.0985
Biological	biomass_bio_0.05	0.1063	0.1111	0.0969
Biological	atp_atp_100.0	0.1063	0.1111	0.0969
Biological	biomass_bio_0.2	0.1026	0.1111	0.1008
Topological	local_k5	0.0866	0.0000	0.1105
Topological	local_k3	0.0851	0.0000	0.0959
Topological	local_k4	0.0799	0.1000	0.0806

Bold indicates the top-ranked method and its best scores.

Finally, we evaluated the impact of biological resolution on literature concordance to determine which aggregation metric best preserves the metabolic signatures of canonical pathways. As summarized in Table 9, Pathway_min emerged as the top-performing resolution with global mean (0.1445) and median (0.1213) F1-scores, followed by Pathway_max (0.1198) and Pathway_median (0.1182). These results indicate that rate-limiting bottlenecks (Pathway_min) provide the most consistent representation for both mathematical disease classification and alignment with the literature.

Table 9.

Global benchmark of biological resolutions against literature ground truths, aggregating retrieval F1-scores across five diverse pathologies and ranking resolutions by global mean F1-score.

Biological resolution	Global mean F1	Global median F1	Std. dev
Pathway_min	0.1445	0.1213	0.1218
Pathway_max	0.1198	0.1111	0.0870
Pathway_median	0.1182	0.1176	0.0796
Pathway_sum	0.1044	0.1111	0.0959
Pathway_mean	0.1034	0.1111	0.0941

Bold indicates the top-ranked resolution and its best scores.

Discussion

The findings of this benchmark indicate that accurate metabolic phenotyping is driven by the isolation of specific systemic constraints rather than aggregate network activity. The global dominance of the Pathway_min resolution suggests that metabolic signals are highly localized [62]. Our results demonstrate that predictive accuracy is not a function of data volume, but rather the quality and relevance of the selected features. By excluding the majority of the flux space, the framework effectively discards stochastic noise and focuses on the specific metabolic steps that are most sensitive to disease-induced perturbations. In the diseases examined here, the disease state was frequently better characterized by its restrictive bottlenecks than by its statistical average of its flux distributions. Because many pathologies involve distributed metabolic changes, we do not claim this as a universal biological principle.

The efficacy of the Pathway_min resolution suggests that identifying the point of maximal restriction, biochemically defined as the rate-limiting step [63], can provide more informative signals than aggregate pathway behavior. In many diseased states, metabolic dysfunction is not distributed uniformly across a subsystem but is instead localized at specific enzymatic junctions [64]. Our findings indicate that central tendency measures, such as Pathway_mean, may dilute these localized perturbations by averaging them with reactions that remain passive or are governed by nonspecific stoichiometric noise. By isolating the minimum flux, the framework focuses on the “weakest link” of the metabolic sequence, revealing that these primary points of failure can convey more precise messages about the regulatory state of the cell than the total or average output of the pathway.

Under leakage-free evaluation, diagnostic accuracy was largely insensitive to feature density: reducing the feature space to the top 10% neither improved nor substantially degraded performance relative to the full network (a difference of ∼0.01 at the Reaction resolution and <0.001 at Pathway_min). This indicates that the diagnostic signal is concentrated in a small, robust feature core, so that the majority of reactions are redundant rather than actively harmful. Feature selection therefore acts primarily as a dimensionality-reduction step that preserves accuracy [65], rather than as a denoising mechanism required to recover performance.

Model architecture nonetheless modulated the response to feature density. Logistic Regression was the only classifier to lose accuracy at full density (a ∼2.7% decline), consistent with the Curse of Dimensionality [19] affecting a purely linear decision boundary, whereas SVM was essentially unaffected and tree-based ensembles slightly improved with additional features [66]. Feature selection is therefore beneficial primarily for Logistic Regression rather than a strict requirement across linear models.

The near-identical performance of ANOVA and Wilcoxon, despite only moderate agreement in their selected feature sets (Cohen’s κ = 0.50), demonstrates a state of diagnostic equifinality. This indicates that the framework’s accuracy is not dependent on a specific set of biomarkers, but rather on a systemic signal distributed across the network. The partial compositional overlap suggests that metabolic networks contain redundant information paths [67]; ANOVA and Wilcoxon prioritize partly divergent flux signatures that remain equally representative of the same disease phenotype. This allows the framework to maintain stability regardless of the statistical assumptions of the selection filter.

The integration of objective coefficients () alongside computed fluxes provides a performance gain that is inversely proportional to biological resolution. While fluxes represent the realized metabolic output, captures the mathematical constraints that define the regulatory intent [68]. Our results show that the gain from including these coefficients doubles when transitioning from the Reaction to the Pathway level. This indicates that acts as an information recovery mechanism; as aggregation hides the granularity of individual reactions, the explicit inclusion of objective weights restores the regulatory context necessary for accurate classification.

The results show a clear trade-off between topological precision and robustness. The robust_sigma family provides global stability, while local_k methods act as high-risk specialists. Denoising the results matrix caused an 11-rank jump for local_k3 and local_k4. This proves they are highly sensitive topological estimators. These objectives offer high resolution in high-signal contexts like BC and BRCA [69]. However, their performance degrades in systemic disorders (e.g. Alzheimer’s, Diabetes), where metabolic dysregulation is globally distributed across the network rather than confined to specific topological hubs.

Robust optimization, however, functions as a domain-agnostic generalist strategy. It ensures consistent performance across all disease types by regularizing flux variance. This stability comes at the cost of extreme performance peaks. Our findings show that topological expansion is not a universal advantage. It is a specialized tool that requires a high signal-to-noise ratio to be effective. For general clinical pipelines, statistical regularization remains a default strategy for reliability.

Biological validation and mechanistic interpretation

The transcriptomic validation reveals a fundamental principle of mechanistic sufficiency. While the Pathway_max resolution aligns with the broad upregulation signals often detected in gene expression studies, its failure to improve predictive accuracy suggests that maximum flux capacity is a secondary feature. In contrast, the statistical parity (P>.90) between the predictively superior Pathway_min and the standard Pathway_mean confirms that the rate-limiting bottleneck alone is biologically sufficient to represent the regulatory state of the entire pathway. This implies that the diagnostic information of a metabolic subsystem is systemically represented by its most constrained reaction, rendering the remaining flux data redundant for diagnostic classification.

The comparative analysis of model architectures reveals a significant performance advantage for linear classifiers (Logistic Regression) over tree-based ensembles (Random Forest [13], XGBoost [14]) in retrieving the canonical ground truth pathways (P <.001). This disparity is rooted in the methodological nature of the reference pathways. Canonical metabolic markers established in the literature are predominantly identified through univariate statistical frameworks that evaluate pathways independently [70, 71]. Logistic Regression inherently aligns with this structure, as its mathematical optimization assigns additive weights to capture main, independent effects. On the other hand, tree-based models partition the feature space to capture nonlinear, conditional dependencies between multiple variables [66]. The lower overlap score of Random Forest therefore indicates that tree-based ensembles prioritize combinatorial metabolic interactions that do not strictly align with lists composed of canonical pathways.

The analysis demonstrated that the choice of objective function, such as ATP maximization or robust optimization, did not significantly alter the retrieval of canonical pathways (P =.074). This indicates that the feasible flux space is fundamentally constrained by the baseline stoichiometric topology of the Recon3D network [72], making external optimality assumptions largely redundant for feature selection. It is important to distinguish between two distinct roles of the objective function: while it measurably affects diagnostic classification performance (where robust_sigma is the most reliable generalist), it has a minimal effect on canonical-pathway retrieval and biological interpretation, which are instead dominated by patient-specific data integration () and the network’s stoichiometric topology. These two findings are complementary rather than contradictory. In contrast, incorporating metabolomics-derived reaction coefficients () into the model yielded an improvement in literature concordance (). Together, these findings validate a core premise of our methodology: the accuracy of patient-specific data integration () is associated with biological concordance more strongly than the mathematical formulation of the objective function. Rather than relying on generic optimality goals, utilizing metabolomics evidence successfully restricts the theoretical stoichiometric space into a clinically relevant, patient-specific metabolic phenotype. To quantify the extent to which alternative optima and numerical nonuniqueness might influence the personalized features, we recomputed the full flux-variability interval width for all 10 600 reactions, across every patient in three cohorts (BRCA, PRAD, and PDAC) and three objective functions, and compared its half-width with the between-patient spread of the corresponding feature. We defined this as an ”ambiguity ratio,” where a value below 1 indicates that the uncertainty from alternative optima is smaller than the biological signal utilized by the classifier. For approximately two-thirds of the active reactions, this ratio fell below 0.1 (pooled median 0.038; BRCA 0.029, PRAD 0.038), demonstrating that alternative-optima uncertainty accounts for <10.

Limitations

This benchmark has several limitations. First, we utilized the global Recon3D metabolic network model [1]. While Recon3D provides comprehensive coverage, tissue-specific reconstructions could improve topological precision for localized pathologies [73]. Second, our framework relies on steady-state assumptions. Metabolomic snapshots capture a specific moment in time, but the underlying FVA logic assumes metabolic equilibrium. Integrating longitudinal cohorts or dynamic simulation frameworks [74] may account for the temporal shifts that steady-state models currently omit. Third, while we use metabolite fold changes to compute the coefficients, the framework does not yet integrate proteomics data. Including enzyme abundance would provide a direct bridge between the measured metabolites and simulated flux rates [75]. Finally, while the framework identifies critical metabolic bottlenecks, these computational findings warrant experimental validation to confirm their physiological relevance and clinical utility. Our biological validation relies on transcriptomic concordance and curated-literature agreement, and thus lacks independent experimental confirmation, which remains necessary to establish definitive physiological relevance. In addition, all preprocessing steps used to derive the reported estimates, including feature selection and standardization, were computed within training folds only, thereby preventing the evaluation bias that can arise when cohort-level quantities are estimated prior to fold splitting.

Conclusions

This study establishes a comprehensive benchmarking framework for personalized metabolic modeling by evaluating 57 600 experimental configurations across diverse disease etiologies. The global superiority of the Pathway_min resolution indicates that the rate-limiting step serves as the most reliable diagnostic signal within a metabolic pathway. Diagnostic accuracy was largely insensitive to the feature-density threshold, so restricting the feature space provides dimensionality reduction without a substantial change in accuracy relative to full-network representations. Furthermore, the integration of objective function coefficients () serves as a crucial information recovery mechanism, preserving the regulatory context that is otherwise lost during biological aggregation.

While certain objective functions achieve peak performance in specific diseases, statistical regularization (robust_sigma) emerges as the most reliable generalist strategy, serving as the optimal default when dataset quality or topological characteristics are unknown. Additionally, tree-based ensembles were robust across feature densities, while among linear models only Logistic Regression showed a modest benefit from feature selection. By systematically quantifying the impact of these methodological choices, this benchmark provides a standardized reference to guide the reliable design and execution of future metabolic modeling studies.

Across 57 600 experimental configurations, metabolic phenotypes in the studied datasets were best characterized by rate-limiting constraints rather than maximum flux capacities. The superior predictive performance of the Pathway_min resolution, combined with its statistical parity to mean activity in transcriptomic validation, confirms that the bottleneck reaction is biologically sufficient to represent pathway regulation. In contrast, the failure of maximum flux representations to align with biological ground truths indicates that peak capacity is a redundant feature for diagnostic classification.

Biological validation further reveals that the mathematical formulation of the objective function exerts no statistically significant influence on the retrieval of canonical cancer pathways. Instead, the feasible solution space is fundamentally constrained by the stoichiometric topology of the network and the integration of patient-specific metabolomic constraints (). Therefore, the diagnostic accuracy of the metabolic model depends on the precision of data integration rather than the selection of a generic optimization goal. Finally, the observed alignment between linear classifiers and literature-derived biomarkers strictly reflects the univariate statistical origins of the reference pathways, indicating that tree-based nonlinear models prioritize combinatorial interactions that are distinct from these traditional, independent features.

Key Points

• Pathway-level minimum reaction flux (bottlenecks) provides the optimal diagnostic signal for metabolic phenotyping, outperforming aggregate metrics.

• Diagnostic accuracy is largely insensitive to feature density; aggressive feature selection is not required and yields only a modest benefit for linear models.

• Tree-based ensembles are robust to high-dimensional flux data; among linear models, only Logistic Regression benefits modestly from feature selection.

• Integrating patient-specific objective function coefficients () as features restores regulatory context lost during biological aggregation.

• Statistical regularization provides a robust, generalist approach for multi-disease modeling compared with highly sensitive topological methods.

Author contributions

Mehmet Ali Erdoğan (Conceptualization, Investigation, Methodology, Writing—original draft) and Ali Cakmak (Supervision, Writing—review & editing). All authors read and approved the final manuscript.

Conflicts of interest

The authors declare that they have no competing interests.

Funding

This work was supported by the Scientific and Technological Research Council of Türkiye (TÜBİTAK)—EU Joint Programme—Neurodegenerative Disease Research (JPND) [grant number 124N069]; the Scientific Research Projects Unit of Istanbul Technical University (ITU BAP) [grant number TGA-2025-46998]; and the National Center for High-Performance Computing (UHEM) [grant number 1009742021].

Data availability

The results published here are in whole or in part based on data obtained from the AD Knowledge Portal (https://adknowledgeportal.org). The Alzheimer’s disease data (ROSMAP) was accessed via Synapse ID: syn3219045, and the Diabetes data (DiCAD) was accessed via Synapse ID: syn9944859. All other datasets are metabolomics datasets available from their respective original publications: BC [7], and the BRCA, PRAD, and PDAC tumor-atlas cohorts [8]. The transcriptomic data, utilized exclusively for independent biological validation, were obtained from the same multimodal tumor-metabolism atlas [8]. The custom source code, scripts, and computational pipelines generated during the current study are available in the GitHub repository: https://github.com/MaliErdgn/Benchmark-Metabolitics.